It is known that a machine for producing cardboard tubes basically comprises:                means for continuously feeding two or more ribbons made of paper or similar material, at least one ribbon being provided with a predetermined amount of glue in correspondence of one of its sides, the ribbons being drawn from corresponding bobbins which are supported by the feeding means;        belt type means, which are positioned downstream of the feeding means, for winding and advancing the ribbons onto a spindle, forming a plurality of spirals which are overlapped and staggered according to a predetermined staggering step, so that the tube results from the reciprocal overlapping and gluing of the ribbons which are spirally wound on the spindle;        means, which are positioned downstream of the spindle, for cutting the continuous tube into elements having a predetermined length.        
The first ribbon, i.e. the ribbon destined to directly contact the spindle, is not glued, to avoid its adhesion to the spindle surface.
In practice, the belt means, which are positioned onto the spindle downstream of with respect to the feeding direction of the ribbons, drawn the ribbons by exerting on them a traction force which is directed towards the spindle and, while it is forming, the tube made by the overlapped spiral ribbons advances and rotates about the longitudinal axis of the spindle.
The intervention rate of the cutting means depends on the advancing speed of the tube onto the spindle and on the predetermined length of the elements obtained from the tube.
Such a machine is described in WO 95/10400 and WO 95/10399.
One of the main drawbacks deriving from of such machines lies in a cleavage of the tube in correspondence of the cut sections. This drawback is even more evident when the operative speed of the machine increases.